Key Sequence

Notation

New Concepts

• random variables of interest
  • binomial distribution
  • Bernoulli distribution

Important Results / Claims

• New problem solving recipe
  • recognize classic random variable
  • define a random variable of the correct parameters
  • use their PMF and solve
• Galton Board

Questions

Debugging probability: put in large values of \(p\) for things; if you end up with a number higher than \(1\) for the probability, you probably tried to add not mutually exclusive events

Interesting Factoids

Key Sequence

Notation

New Concepts

• e
• variance
• poisson distribution

Important Results / Claims

• probability of k in x time

Questions

Interesting Factoids

Key Sequence

Notation

New Concepts

• support
• more discrete random variables!
  • geometric random variable
  • negative binomial distribution
• hypergeometric: drawing without replacement
• probability density function
• continuous random variables
  • uniform distribution
  • exponential distribution
• cumulative distribution function

Important Results / Claims

• PDFs are derivatives of probability

Questions

Interesting Factoids

Key Sequence

Notation

New Concepts

Important Results / Claims

Questions

Interesting Factoids

Key Sequence

Notation

New Concepts

• multinomial coefficient
• joint probability distribution
• probablistic models
  • multinomial distribution
• text Naive Bayes

Important Results / Claims

• for Naive Bayes against some multinomial distribution, its often a good time to find the ratios of the results because the combination in the beginning cancels out if you are analyzing the same samples upon different prior probabilities

\begin{equation} \frac{P(H|D)}{P(M|D)} = \frac{\prod_{i} h_{i}^{c_{i}}}{\prod_{i} m_{i}^{c_{i}}} \end{equation}

Questions

Interesting Factoids